Han Carlson Adder(Professor Han invented Han Carlson adder in part of his Ph. D. dissertation). currently widely used in Intel Pentium Micro. Download scientific diagram | (a) Han-Carlson (HC) adder; from publication: Power-aware Design of Logarithmic Prefix Adders in Sub-threshold Regime: A. Key Words – Parallel Prefix Adders, Han-Carlson Adder, area, prefix computation, Power Consumption, delay. 1. Introduction. VLSI binary adders are critically.

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A constant-coefficient multiplier is given as a part of MACs as follow. The carry-save form is converted to the corresponding binary output by an FSA. Generalized MAC Figure The RB addition tree is closely related to 4;2 compressor tree.

The equation can be interpreted as stating that there is a carry either if one is generated at that stage or if one is propagated from the preceding stage. Therefore, let Gi and Pi denote the generation and propagation at the ith stage, we have: Figure 7 is the parallel prefix graph of a Brent-Kung adder.

This adder structure has minimum logic depth, and full binary tree with minimum fun-out, resulting in a fast adder but with a large area. Dadda tree is based on 3,2 counters. To reduce the hardware complexity, we allow the use of 6,35,34,33,2and 2,2 counters in addition to 7,3 counters. A block carry look-ahead adder BCLA is based on the above idea.

These hardware algorithms are also used to generate multipliers, constant-coefficient multipliers and multiply accumulators.

The n-operand array consists of n-2 carry-save adder. Figure 3 shows the parallel prefix graph of a bit BCLA, where the symbol solid circle indicates an extension of the fundamental carry operator described at Parallel prefix adders.

This optimal organization of block size includes L blocks with sizes k1, k2, To reduce the hardware complexity, we allow the use of 2,2 counters in addition to 3,2 counters. The fixed block size should be selected so that the time for the longest carry-propagation chain can be minimized. If there are five or more blocks in a RCLA, 4 blocks are grouped into a single superblock, with the second level of look-ahead applied to the superblocks.


Overturned-stairs tree requires smaller number of wiring tracks compared with the Wallace tree and has lower overall delay compared with the balanced delay tree.

The complexity of multiplier structures significantly varies with the coefficient value R. Each group generates two sets of sum bits and an outgoing carry.

The adder structure is divided into blocks of consecutive stages with a simple ripple-carry scheme. This signal can be used to allow an incoming carry to skip all the stages within the block and generate a block-carry-out.

The hardware algorithms for constant-coefficient multiplication are based on multi-input 1-output addition algorithms i. Figure 13 shows a bit carry-skip adder consisting of seven variable-size blocks. Figure 14 compares the delay information of true paths and that of false paths in the case of Hitachi 0. Once the incoming carry is known, we need only to select the correct set of outputs out of the two sets without waiting for the carry to further propagate through the k positions.

Book Chapter – Han Carlson Adder – MSL

Figure 2 shows the parallel prefix graph of a bit RCLA, where the symbol solid circle indicates an extension of the fundamental carry operator described at Parallel prefix adders. At present, the combination of CSD Canonic Signed-Digit coefficient encoding technique with the SW-based PPAs seems to provide the practical hardware implementation of fast constant-coefficient multipliers. A ripple-block carry look-ahead adder RCLA consists of N m-bit blocks arranged in such a way that carries within blocks are generated by carry look-ahead but carries between blocks are rippled.

Balanced delay tree requires the smallest number of wiring tracks but has the highest overall delay compared with the Wallace tree and the overturned-stairs tree.

Another way to design a practical carry look-ahead adder is to reverse the basic design principle of the RCLA, that is, to ripple carries within blocks but to generate carries between blocks by look-ahead.

There are many possible choices for the multiplier structure for a specific coefficient R. Figure 19 shows an operand 4;2 compressor tree, where 4;2 indicates a carry-save adder carlosn four multi-bit inputs and two multi-bit outputs.


Hardware algorithms for arithmetic modules

You can further increase the number of product terms computed in a single cycle depending on your target applications. In other words, a carry is generated if both operand bits are 1, and an incoming carry is propagated if one of the operand bits is 1 and the other is 0.

In this generator, we employ a minimum length encoding based on positive-negative representation. A parallel prefix adder can be represented as a parallel prefix graph consisting of carry operator nodes. In this generator, the group lengths follow the simple arithmetic progression 1, 1, 2, 3, The fundamental carry operator is represented as Figure 4.

On the other hand, the structure b shows a faster design, where two product terms are computed simultaneously in a single iteration. Each set includes k sum bits and an outgoing carry. The Booth recoding of the multiplier reduces the number of partial products and hence has a possibility of reducing the amount of hardware involved and the execution time. The idea of the ripple-block carry look-ahead addition is to lessen the fan-in and fan-out difficulties inherent in carry look-ahead adders.

Figure 5 is the parallel prefix graph of a Ladner-Fischer adder. Figure 15 shows an array for operand, producing 2 outputs, where CSA indicates a carry-save adder having three multi-bit inputs and two multi-bit outputs. This reduces the ripple-carry delay through these blocks. The block size m is fixed to 4 in the generator. Wallace tree is known for their optimal computation time, when adding multiple operands to two outputs using carry-save adders.

Hardware algorithms for arithmetic modules

This process can, in principle, be continued until a group of size 1 is reached. AMG provides constant-coefficient multipliers in the form: Please note that the delay information of carry-skip adders in Reference data page is simply estimated by using false paths instead of true paths. These expressions allow us to calculate all the carries in parallel from adde operands.